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高维系统周期解的存在性与唯一性
EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF HIGHER DIMENSIONAL SYSTEMS
【摘要】 本文首先利用一种新方法讨论高维系统解的一致有界性,一致最终有界性及非常稳定性问题,然后将所获结果应用于高维系统周期解的存在性与唯一性的研究.另外,木文还提出了“阶梯形系统”的概念,并对其建立了一种利用系统部分方程周期解存在性判定整个系统周期解存在性的方法.
【Abstract】 in this paper, we first use a new method to obtain some new results concerningthe uniform boundedness, uniformly ultimate boundedness and extreme stability of solutionsof higher dimensional systems. And then using these results we study the etistence anduniqueness of periodic solutions of higher dimensional systems. On the other hand, we alsointroduce the concept of "ladderlike system" and present an approach to study the existenceof periodic solutions for such system.
【关键词】 高维系统;
周期解;
一致有界性;
一致最终有界性;
非常稳定性;
【Key words】 Higher dimensional system; periodic solution; uniform boundedness; uniformly ultimate boundedness; extreme stability;
【Key words】 Higher dimensional system; periodic solution; uniform boundedness; uniformly ultimate boundedness; extreme stability;
【基金】 国家自然科学基金
- 【文献出处】 应用数学学报 ,ACTA MATHEMATICAE APPLICATAE SINICA , 编辑部邮箱 ,1996年01期
- 【分类号】O175.1
- 【被引频次】1
- 【下载频次】73